Problem: Simplify the following expression: $\sqrt{117}-\sqrt{13}+\sqrt{52}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{117}-\sqrt{13}+\sqrt{52}$ $= \sqrt{9 \cdot 13}-\sqrt{13}+\sqrt{4 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{13}-\sqrt{13}+\sqrt{4} \cdot \sqrt{13}$ $= 3\sqrt{13}-\sqrt{13}+2\sqrt{13}$ Finally, simplify by combining the terms. $= ( 3 - 1 + 2 )\sqrt{13} = 4\sqrt{13}$